properties of cube, cuboid, prism & pyramid
TRANSCRIPT
SOLID FIGURESOLID FIGURE
• CUBE CUBE • CUBOIDCUBOID. PRISM. PRISM
. PYRAMID. PYRAMID
CUBE
A
H
E F
D C
B
G
ss
s
S = edge
face
AC = face diagonalCE = space diagonalACGE = diagonal plane
A
H
E F
D C
B
G
ss
s S = edge
face
AC = face diagonalCE = space diagonalACGE = diagonal plane
CUBOID
A
H
E F
DC
B
G
l
h
w
h
l
AG= space diagonal
ABGH= plane of diagonal
VOLUME OF A CUBEEach cube has equal edgeslength = width = height, Then the volume of a cube:Volume = edge x edge x edgeIf s = edge of a cubeWe getVolume = S x S x S = S3 Hence V = S3
A
H
E F
D C
B
G
SURFACE AREA OF A CUBE
Each cube consist of 6 squared faces which have equal area.
Area = 6 x S x S
= 6 S2
So, A = 6 S2
A
H
E F
D C
B
G
S
S
S
VOLUME OF A CUBOIDEach cuboid has: length (l), width (w) and height (h).
Volume = l x w x h = lwh
So, V = lwhA
H
E F
D C
B
G
SURFACE AREA OF A CUBOID
A1 = 2 x l x w
A2 = 2 x l x h
A3 = 2 x w x h
A
H
E F
D C
B
G
SURFACE AREA OF A CUBOID
Surface area of a cuboid:
Area = A1 + A2 + A3
= 2lw + 2lh + 2wh = 2 (lw + lh + wh)
A
H
E F
D C
B
G
EXAMPLE 1
Calculate the volume and the surface area of a cube whose the length of the edges is as the following:
a. 6 cm
b. 10 cm
c. 15 cm
d. 20 cm.
SOLUTION
a. S = 6 cm.
V = S3
= 6 x 6 x 6
= 216 cm3
A = 6 S2
= 6 x 6 x 6
= 216 cm2
SOLUTION
b. S = 10 cm.
V = S3
= 10 x 10 x 10
= 1.000 cm3
A = 6 S2
= 6 x 10 x 10
= 600 cm2
SOLUTIONc. S = 15 cm.
V = S3
= 15 x 15 x 15
= 3.375 cm3
A = 6 S2
= 6 x 15 x 15
= 1.350 cm2
SOLUTION
d. S = 6 cm.
V = S3
= 20 x 20 x 20
= 8.000 cm3
A = 6 S2
= 6 x 20 x 20
= 2.400 cm2
EXAMPLE 2
Calculate the volume and the surface area of a cuboid whose the length of the edges:a. l = 12 cm, w = 8 cm, h = 6 cm
b. l = 15 cm, w = 12 cm, h = 8 cm
SOLUTION
a. l = 12 cm, w = 8 cm, h = 6 cm V = l . w . h = 12 x 8 x 6 = 576 cm3 A = 2 (lw + lh + wh) = 2 (12 x 8 + 12 x 6 + 8 x 6) = 2 (96 + 72 + 48) = 2 x (216) = 432 cm2
SOLUTIONb. l = 15 cm. w = 12 cm, h = 8 cm
V = l . w . h
= 15 x 12 x 8
= 1.440 cm3
A = 2 (lw + lh + wh)
= 2 (15 x 12 + 15 x 8 + 12 x 8)
= 2 (180 + 120 + 96) = 2 x (396)
= 792 cm2
EXERCISE - 1
Calculate the volume of a cuboid whose height is 20 cm and the base is in the form of a square whose side is 7 cm long
Solution
Given : the length of its base = 7 cm
height = 20 cm
Volume = Base area x height
= (7 cm x 7 cm) x 20 cm
= 980 cm3
So, the volume of the cuboid is 980 cm3.
EXERCISE - 2
Calculate the volume and the surface area of a cube whose face diagonal is cm 24
Solution
Given:Face diagonal = cm
then The length of the edge = 4
V = 43
V = 64So, the volume of the cube is 64 cm3
24
Solution
Given:Face diagonal = cm
then The length of the edge = 4
A = 6 x 4 x 4V = 96
So, the surface area of the cube is 96 cm3
24